10¹⁵ Gauss — that's the magnetic field found on some white dwarfs. It is billions of times stronger than what a compass shows on Earth. A white dwarf is not a star in the usual sense, but a cooled core the size of a planet. Inside, gravity opposes the pressure of degenerate electrons. But under an ultra-strong field, this pressure ceases to be uniform — like an invisible corset squeezing the star.
Transverse electron motion becomes quantized into levels discovered by Lev Landau, and the pressure along the field lines becomes greater than across them. Anisotropy arises — a directed force that compresses the dwarf. To understand how tightly the corset is laced, physicists built an equation of state for the electron-ion gas, taking into account quantized orbits, Coulomb interactions between particles, and even nuclear transformations during electron capture.
This data was fed into the generalized equations of Subrahmanyan Chandrasekhar and Tolman–Oppenheimer–Volkoff, which describe gravitational equilibrium with different pressures radially and tangentially. Numerical integration for different central densities yielded families of equilibrium stars.
The picture was confirmed. At B/Bc=1, the transverse pressure turned out to be systematically smaller, especially in the envelope. The anisotropic term acts as an additional compressive force: radii shift downward. For example, a carbon white dwarf of maximum mass 1.385 solar masses contracted by 40 km — about 4%. Importantly, the mass limit found by Chandrasekhar hardly changes: variations are fractions of a percent. In the center, the density is so high that many levels are filled, and anisotropy smoothes out — the corset weakens closer to the core.
Comparison with the Montreal database shows that accounting for anisotropy improves the agreement of theory with observations. Some compact massive objects now receive a natural explanation without exotic hypotheses. Ignoring the magnetic corset can lead to systematic errors in radius determination, which is critical for stellar evolution models. Thus, the quantum corset of Landau levels adds the final touch to the structure of magnetic white dwarfs. A star compressed by directed pressure becomes more compact, but remains within the bounds predicted back in 1930.
If the magnetic field in a typical white dwarf increased the anisotropy by only 10%, its radius would shrink by several percent, which is equivalent to an increase in average density of tens of tons per cubic centimeter — that's how important the quantum "corset" is.